A new (2+1)-dimensional differential-difference equation is considered. With the aid of the nonlinearization of the Lax pair, the (2+1)-dimensional differential-difference equation is decomposed into a new integrable symplectic map and a class of finite-dimensional integrable Hamiltonian systems. Based on the theory of algebra curve, the continuous flow and discrete flow are straightened out in view of the introduced Abel–Jacobi coordinates.
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